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Spatiotemporal progression of metastatic breast cancer: a Markov chain model highlighting the role of early metastatic sites

Spatiotemporal progression of metastatic breast cancer: a Markov chain model highlighting the... www.nature.com/npjbcancer All rights reserved 2374-4677/15 ARTICLE OPEN Spatiotemporal progression of metastatic breast cancer: a Markov chain model highlighting the role of early metastatic sites 1,2 3 4 4 5 6 4 Paul K Newton , Jeremy Mason , Neethi Venkatappa , Maxine S Jochelson , Brian Hurt , Jorge Nieva , Elizabeth Comen , 4 3 Larry Norton and Peter Kuhn BACKGROUND: Cancer cell migration patterns are critical for understanding metastases and clinical evolution. Breast cancer spreads from one organ system to another via hematogenous and lymphatic routes. Although patterns of spread may superficially seem random and unpredictable, we explored the possibility that this is not the case. AIMS: Develop a Markov based model of breast cancer progression that has predictive capability. METHODS: On the basis of a longitudinal data set of 446 breast cancer patients, we created a Markov chain model of metastasis that describes the probabilities of metastasis occurring at a given anatomic site together with the probability of spread to additional sites. Progression is modeled as a random walk on a directed graph, where nodes represent anatomical sites where tumors can develop. RESULTS: We quantify how survival depends on the location of the first metastatic site for different patient subcategories. In addition, we classify metastatic sites as “sponges” or “spreaders” with implications regarding anatomical pathway prediction and long-term survival. As metastatic tumors to the bone (main spreader) are most prominent, we focus in more detail on differences between groups of patients who form subsequent metastases to the lung as compared with the liver. CONCLUSIONS: We have found that spatiotemporal patterns of metastatic spread in breast cancer are neither random nor unpredictable. Furthermore, the novel concept of classifying organ sites as sponges or spreaders may motivate experiments seeking a biological basis for these phenomena and allow us to quantify the potential consequences of therapeutic targeting of sites in the oligometastatic setting and shed light on organotropic aspects of the disease. npj Breast Cancer (2015) 1, 15018; doi:10.1038/npjbcancer.2015.18; published online 21 October 2015 INTRODUCTION all are based (typically) on a single snapshot of patient information in time and mostly obtained only at the primary tumor location It is widely appreciated that cancer is a multifaceted disease when clinically detectable, hence have limited predictive power comprised of distinct biochemical, biomechanical, molecular, age, with respect to forecasting of disease progression and survival. In gender, race, and environmental factors, all of which contribute other forecasting settings (e.g., weather prediction), it is widely directly or indirectly to uncontrolled cell growth, survival, motility, 1–5 appreciated that collecting data at multiple spatial locations and dissemination, and colonization, which in turn effect long-term at multiple time points gives far superior forecasting capability survival of patients. The complex interplay of all of these factors is (even if at lower resolution than a single site) as from these, one is poorly understood, which hinders our ability to accurately predict able to obtain estimates of time derivatives (velocities), and spatial and optimally influence outcomes throughout the course of gradients, facilitating better estimates not just of the current disease progression. As breast cancer spreads from one organ to localized state, but the future distributed state. another via hematogenous and lymphatic routes, cell migration In this paper, we explore the possibility that although breast patterns are critical for understanding metastasis and clinical cancer progression in individuals where little additional clinical evolution, but these patterns are commonly dismissed as information is known can be viewed as unpredictable, metastasis unpredictable in the absence of detailed clinical and patient- patterns assembled over populations of patients that incorporate specific contextual information. As a consequence, comprehensive quantitative statistical forecasting tools to aid in medical decision both temporal and spatial information can be used as a firm basis making have been slower to develop than in other fields, such as for predictive modeling and provides an essential step in financial forecasting and weather prediction. For breast cancer, developing computer-assisted forecasting tools. One of the simplest and most effective dynamical modeling assumptions the main prognostic factors in current use include tumor size, used in this paper is the Markov assumption that progression from patient age, lymph node status, histologic type of tumor, pathologic grade, and hormone-receptor status, and when one anatomical location to another proceeds as a weighted 8–19 available, genetic profiling can also be used effectively. But random walk on a directed graph, with no history dependence 1 2 Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA, USA; Department of Mathematics, University of Southern California, 3 4 Los Angeles, CA, USA; Department of Biological Sciences, Dornsife College of Letters, Arts and Sciences, University of Southern California, Los Angeles, CA, USA; Memorial Sloan 5 6 Kettering Cancer Center, New York, NY, USA; University of Colorado School of Medicine, Aurora, CO, USA and Norris Comprehensive Cancer Center, Keck School of Medicine, University of Southern California, Los Angeles, CA, USA. Correspondence: PK Newton (newton@usc.edu) Received 8 September 2015; accepted 9 September 2015 © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited Spatiotemporal progression of metastatic breast cancer PK Newton et al other than the fact that the tumor initiates in the breast. Although Markov chains not exact, the Markov assumption has been used effectively for a A Markov chain dynamical system is a discrete-time stochastic process: 20–23 lung cancer data set. ! ! v ¼ v A; ðk ¼ 0; 1; 2; ¼Þ Formed by the longitudinal data set of 446 breast cancer kþ1 k patients from Memorial Sloan Kettering Cancer Center assembled ! where A is an nxn transition matrix and v is a state vector whose entries over a 25-year period, the Markov transition probabilities indicate the probability of a metastatic tumor developing at each of the n from site to site are estimated for each of the groups anatomical sites, at time step k. The time step k represents spread from estrogen receptor (ER)+/human epidermal growth factor receptor one site to the next in a patient, which can be calibrated with data. The 2 (HER2) −,ER − /HER2 − , and HER2+. We show that survival initial state vector in our model is given by v ¼ð1; 0; 0; 0; ¼ Þ, where the depends on the location and characteristics of the first metastatic first entry corresponds to the breast location, indicating that initially there is a tumor located in the breast with probability 1, and no other metastatic site to which the disease spreads. In fact, the data show that tumors at the other locations. The transition matrix A has entries whose survival characteristics that use this dynamical and spatial rows sum to one (corresponding to the fact that they represent information are potentially as predictive as the ER/HER2 status probabilities of transition and hence must sum to one), and the ijth entry, of a patient. Stated differently, we use information not only on a , indicates the probability of metastatic disease spreading from site “i” to ij static characteristics of the primary tumor taken as a snapshot in site “j”. We refer the reader to Norris for a comprehensive introduction to time but also dynamical information on where the disease is Markov chains and refs 20–23 for recent applications of Markov modeling spreading, and associated characteristics of the first metastatic in the context of lung cancer metastasis. As the longitudinal data are site. The location and character of this first site, in turn, have relatively time resolved over long periods, the entries of the transition important consequences on the locations and time sequence of matrix are obtained in a straightforward empirical way by simple subsequent metastatic sites, influencing timescales of disease denumeration of disease progression events from one anatomical site to the next in each of the patients in a cohort (see ref. 25 for more general progression and survival. The full panel of spatiotemporal discussions). For example, in tracking a cohort of 100 patients with a diagrams and models for each subgroup is available for further primary breast tumor only, if 36 of them subsequently develop their first study on the interactive website. Additional information metastatic tumor in the bone, then the transition probability from breast to associated with treatment scenarios is also available. bone, obtained empirically, would be 0.36 for this cohort. Note that this number should be interpreted as an estimate based on the length of time the cohort is being followed. In a similar way, by simple denumeration of MATERIALS AND METHODS the distinct metastatic transitions from site to site that each patient Description of data set follows, we can estimate the Markov transition probabilities from any given The time-resolved data contain annotated clinical information on 446 site to any other site to create the Markov transition matrix A, which drives patients from the time of their initial diagnosis of breast cancer between our model dynamics. 1975 and 2009 at Memorial Sloan Kettering Cancer Center. Notably, the majority of patients were originally diagnosed after 1990, with only 2 patients diagnosed initially in 1975 and 1979, and 25 patients diagnosed in the 1980s. RESULTS None of the patients had evidence of metastatic disease at the time of Ten-year progression pathways diagnosis; all of the patients eventually developed metastatic disease. For The panels in Figure 1a show ring diagrams associated with each patient, the database contains all clinical and demographic information 10-year progression representing all patients whom we have a on the patient from the date of their diagnosis and subsequent development of metastatic disease over time. For each patient, metastatic disease is noted minimum of 10 years of continuous data on starting at the time of at the time of diagnosis of metastatic disease, usually first detected by diagnosis. These include patients that were enrolled in the study positron emission tomography imaging and confirmed by biopsy. Patients for more than 10 years and those that were expired before the were then followed with serial positron emission tomography and/or 10-year mark (as we know their metastatic progression after their computed tomography imaging and physical exams. Physical exams were death date). For the remainder of the paper, we will only focus on usually done between 1- and 3-month intervals. Imaging was usually done at those patients that qualify for the 10-year study. The 10-year 3-month intervals. At the time of new metastatic development, site(s) of window was chosen as a balance between having enough disease and the date were noted. The treatment rendered and any other patients for statistical significance (i.e., not too long), yet long pertinent clinical and demographic information is available on each patient. All the relevant information regarding each patient’s original breast cancer enough so that significant progression occurred in the cohort diagnosis, including date of pathology report, type of breast cancer, and under study. The website http://kuhn.usc.edu/breast_cancer/ oncologic and surgical treatment rendered at original diagnosis is noted. All allows for interactive viewing of these diagrams for both shorter of the information on the treatment rendered throughout metastatic disease and longer windows. Figure 1a shows the pathways of the 350 course is documented. The date of last follow-up and whether patients are eligible patients all grouped together over the 10-year window. alive or deceased is also noted. Of the 446 patients, 173 patients were alive as For this group, bone metastases are the most prominent first of 5 January 2013 and 273 had expired. metastatic location, occurring in roughly 35% of the patients being followed. In Figure 2b–d we break the group down into Metastatic progression diagrams subcategories. Figure 1b shows the ER+/HER2 − subgroup Longitudinal data can be organized most usefully in the form of ring (218 patients), where bone metastasis occurs first in roughly diagrams, as shown in Figure 1a for the entire aggregated data set. Disease 40% of all patients. Figure 1c shows the ER − /HER2 − subgroup progression proceeds from the inner pink ring (primary breast tumor) (70 patients), where bone metastases occurs in a little over 25% of outward, with each ring representing a subsequent metastatic tumor, color the patients, and Figure 1d shows the HER2+ subgroup coded according to anatomical site, with a sector size representing the (62 patients) with ~ 33% of patients relapsing first at the bone percentage of patients with tumors at that location. The first ring out from the inner ring in Figure 1a shows that bone is the most prominent first site. Further examination of the sector sizes in the first metastatic metastatic site, in roughly 35% of the patients. The progression of each of ring shows that the second most common first relapse site differs the 350 patients proceeds along a ray. The diagram summarizes the among the subgroups. For the ER+/HER2 − and the ER − / complete pathway history (207 distinct pathways) associated with this HER2 − groups, distant lymph nodes are the second most common group of patients tracked over the duration of 10 years. From this data, we first metastatic site, whereas for the HER2+ subgroup, the second can compute the probability of disease “transition” from one anatomical most common first relapse site is lung/pleura, followed by chest site to any of the others, based on the statistical information contained in wall. The diagrams can be viewed from year to year as gif files on the diagrams. This allows us to estimate the entries of the Markov the interactive website, giving a dynamic view of the disease as it transition matrix associated with disease progression, both in bulk, and for subgroups, which we describe next. progresses from the central pink ring outward. npj Breast Cancer (2015) 15018 © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited Spatiotemporal progression of metastatic breast cancer PK Newton et al Figure 1. Spatiotemporal progression diagram over a 10-year period of subsets of breast cancer patients. The innermost to outermost rings show progression patterns of primary breast cancer patients (pink ring) and formation of metastases (subsequent rings). Circular arc length of each sector represents the percentage of patients with a metastatic tumor in that location. Bone (yellow) is the most common first metastatic site (first ring outside pink). (a) All Patients, (b) ER+/HER2 −,(c)ER − /HER2 − , and (d) HER2+. It should be noted that death is a relatively uncommon Kaplan–Meier curves outcome for a patient with a metastasis to a single organ site, Figure 2 shows Kaplan–Meier survival curves associated with the occurring in only 33.33% of patients in the overall cohort. Though 10-year cohort that we track. Figure 2a shows survival it was notably more common in the HER2+ subgroup of patients curves based on the three subgroups ER+/HER2 − (218 patients), with liver metastasis, and affected 100% of that subgroup. As ER − /HER2 − (70 patients), and HER2+ (62 patients). Note that the expected, the largest number of long-term survivors is recognized ER+/HER2 − subgroup and the HER2+ subgroup show better as ER+/HER2 − patients with bone-only metastasis, with 91.67% of survival trends than the ER − /HER2 − group. these patients remaining alive during the median 10 years of Survival times are measured from the time of initial breast follow-up. Unexpectedly, we also identified that patients with their cancer diagnosis and not from the time of the development of first site of metastasis to lung-only metastasis had a favorable metastatic disease. Patients were treated with Memorial Sloan percentage of patients going on to be long-term survivors Kettering Cancer Center standard of care or appropriate clinical with 68.97% of this subgroup surviving to the end of the trial-based therapy depending on physician recommendations 10-year study period. Of note, the majority of the patients with and patient preferences. Of the HER2+ patients, 87.10% received single lung metastasis as their first presentation of metastasis had trastuzumab-based therapy at some point during their disease ER+/HER2 − disease, only 5 of the patients with a single course. HER2+ patients diagnosed before 15 May 2005 did not lung metastasis at first presentation had triple-negative routinely receive trastuzumab in the adjuvant setting. After this disease. Interestingly, while many of these patients had lung date, most patients did receive herceptin in the adjuvant setting, biopsies to confirm metastatic breast cancer as opposed to a which was noted to significantly improve the outcomes for HER2+ primary lung cancer, they did not routinely undergo resection of breast cancer patients. In the metastatic setting, the Food and the lung metastasis or radiation to the lung. Long-term Drug Administration originally approved trastuzumab in Septem- survivors were also identified in 60.00% of patients with isolated liver metastasis. ber of 1998 (ref. 27). All of the ER+ patients received some form of © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited npj Breast Cancer (2015) 15018 Spatiotemporal progression of metastatic breast cancer PK Newton et al Figure 2. Kaplan–Meier curves showing the survival of breast cancer patients when they initially have no evidence of metastasis to when they progress through their metastatic disease. (a) Comparison of ER+/HER2 −,ER − /HER2 − , and HER2+ patients, (b) patients with a solitary first metastatic site at bone, chest wall, liver, or brain, and (c) subsets of patients with different numbers of first relapse metastases. npj Breast Cancer (2015) 15018 © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited Spatiotemporal progression of metastatic breast cancer PK Newton et al Figure 3. Markov chain networks of metastatic breast cancer shown as circular chord diagrams. Chord widths at their respective starting locations represent one-step transition probabilities between two sites. Primary breast cancer is located on top with metastatic sites ordered clockwise in decreasing order according to transition probability from primary. (a) All patients’ network, (b) all patients’ network highlighting paths connected to the breast, (c) all patients’ network highlighting paths connected to the bone, and (d) all patients’ network highlighting paths connected to deceased. endocrine therapy during the course of their treatment as good an indicator of survival as groupings associated with (i.e.,—tamoxifen, aromatase inhibitor, faslodex). ER/HER2 status. Figure 2c shows survival of patients with multiple Figure 2b shows survival trends based not on these subgroups, early metastases to various sites. Poorest survival are those with but on groupings associated with the location of the first multiple (more than two) first metastases, while much better metastatic site. We focus on four main metastatic sites being survival characteristics are associated with those patients with first bone (87 patients), chest wall (54 patients), liver (21 patients), and metastases that are solitary. brain (5 patients). The patients with first mets to the chest wall The hazard rate of a Kaplan–Meier curve indicates the rate at have the best prognosis, whereas those with first mets to the brain which survival probability is decreasing within the population have the poorest prognosis. Although the 5-year survival of being studied. Computing the hazard ratio between two survival patients with a bone first met is equal to those with a chest wall curves is a good measure of how much better or worse a certain met (around 85%), the 10-year survival is much worse for chest subgroup is doing compared with another. For example, if group wall patients as compared with bone patients (50% vs. 70%, A dies at twice the rate of group B, then the hazard ratio respectively). Patients with first mets at the liver have a poor would be 2. 10-year survival rate (~30%). Definition of a metastasis was based on global clinical Markov chain networks and spreader–sponge diagrams evaluation, which included imaging results, physical examination, Figure 3 shows the Markov diagrams whose transition values are and in many cases, biopsy. However, tissue confirmation of a obtained from the data depicted in the ring diagrams of Figure 1a. metastatic site was not required for the purposes of the model. The breast site is listed at 12:00 in these diagrams, followed in A comparison of Figure 3a, b generally shows that groupings associated with first metastatic location (Figure 2b) gives at least clockwise decreasing order by the most likely first metastatic sites © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited npj Breast Cancer (2015) 15018 Spatiotemporal progression of metastatic breast cancer PK Newton et al Figure 4. Pathway diagrams showing top 30 two-step pathways emanating from breast (pink ring). Nodes are classified as a “spreader” (red) or “sponge” (blue) based on the ratio of the incoming and outgoing two-step probabilities (spreader and sponge factor listed in respective ovals). (a) All patients’ pathway diagram representing 79.8% of total pathways, (b) ER+/HER2 − pathway diagram representing 83.0% of total pathways, (c)ER − /HER2 − pathway diagram representing 81.9% of total pathways, and (d) HER2+ pathway diagram representing 85.5% of total pathways. the patients aggregated (Figure 4a), bone, chest wall, and from the breast. Figure 3a shows the full network diagram clearly depicting the systemic interconnectedness of the anatomical sites mammary lymph nodes are the spreader sites, and lung/pleura, throughout the course of the disease. In these diagrams we also distant lymph nodes, and liver are the sponge sites. In use “deceased” as one of the states in the model and list it in the Figure 4b we show the ER+/HER2 − subgroup with the same last position. The thickness of the paths leaving each of the sites spreader/sponge sites. The amplification factor of bone for this indicates the proportion of transitions from that site to the subgroup (5.421) is particularly high, whereas the absorption receiving site. To clarify this further, we show the outgoing paths factor for liver (0.166) is quite low. For the ER − /HER2 − group from breast (Figure 3b) and bone (Figure 3c). In Figure 3d we show shown in Figure 4c, the mammary lymph nodes seem to be the the paths incoming to the deceased site. strongest spreader (amplification factor of 5.778). Also of some Although the patterns of metastatic spread appear to be highly significance is the brain in this subgroup becomes a sponge, with complex, they can be simplified by examination of respective an absorption factor of 0.392. For the HER2+ subgroup shown in components. The finding on Figure 3b showing that the pathways Figure 4d, lung/pleura and chest wall become the main spreaders, that breast cancer takes out of the breast is significantly less aside from bone. To clarify the spreader/sponge paths more complex than the overall model in Figure 4a suggests that not clearly, Figure 5a–f shows the paths exiting from each of the main only is the primary tumor a source for metastasis but also spreaders (all category), and each of the main sponges. Figure 6a, metastases themselves serve as sources of other metastatic sites d, when viewed together, are instructive in that they show direct and many of these secondary metastases are associated with high significant exchange between spreaders and sponges. For risk of transitioning to death as shown in Figure 3d. example, Figure 5a shows that lung/pleura is the most probable Figure 4 shows the reduced spreader–sponge diagrams for all (sponge) site when exiting bone. Figure 5d, on the other hand, of the patients (Figure 4a), followed by diagrams for each of the shows that cells that exit the lung/pleura site most probably go to subgroups ER+/HER2 −,ER − /HER2 − , HER2+. Sites colored in red liver, another sponge, but they can also go back to bone. are “spreader” sites, whose ratio of outgoing path probability to Prior animal and human experiments have supported the incoming path probability (called the amplification factor) is concept that metastatic sites are seeded and re-seeded with travel greater than one, whereas those colored blue are “sponge” sites, of cancer cells from one site to another via hematogenous 20–21,28 whose ratio of outgoing path probability to incoming path routes; hence flow of cancer cells is likely to be bidirectional probability (called the absorption factor) is less than one. For all of for all metastatic sites. However, the net flow will generally be in npj Breast Cancer (2015) 15018 © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited Spatiotemporal progression of metastatic breast cancer PK Newton et al Figure 5. Spreader/sponge diagrams for all patients showing one-step transition probability from (a) bone, (b) chest wall, (c) LN (mam), (d) lung/pleura, (e) LN (dist), and (f) liver to the top nine sites in the network. Sites are ordered in decreasing order, clockwise, with the spreader/ sponge in question located at 12:00. Outer pink ring represents primary breast cancer and shows the percentage of total transition probability it represents. dist, distant; LN, lymph node; mam, mammary. Of note, very few of these patients underwent pulmonary or the direction from spreader sites to sponge sites. Although therapeutic interventions such as radiotherapy and hormonal hepatic resection or radiotherapy directed at a single organ site. therapy may have the ability to impact trafficking of tumor sites, We suspect that the more likely cause of this difference may be the model did not incorporate differential effects of therapy into the spreader/sponge characteristics of these tumor types in the model and the gradient of metastatic growth is modeled metastatic breast cancer patients. If one examines subgroups, it is based on the population average and standard-of-care noted that for all groups except the triple-negative population, the interventions. An understanding of the impact of therapeutics liver is a more powerful sponge than the lungs, with smaller on the spreader and sponge characteristics of local sites requires transition probabilities for liver than lung in the ER+ and/or HER2+ further investigation. groups. It is within the ER+ and HER2+ groups that there is a low probability of transition from lung metastasis to death, whereas in the triple-negative group, where the transition probability is Metastatic relapse data higher for liver than for lungs that we see an increased risk of It is interesting to go further out in the pathway diagrams. death following development of a lung metastasis. Although in Figure 1a shows that after developing a metastatic tumor at the the absence of a second validation data set, it is possible that bone site, the two most probable second metastatic sites are these findings are artifactual, they raise the possibility that organs lung/pleura, and liver, both representing roughly equal sector that are more “sponge-like” relative to other affected organs are widths (around 10%). But the future prognoses associated with the anatomic sites at highest risk for organ failure leading to those two groups of patients are quite different. In the case of the death. This is particularly true for visceral sites. Interestingly, 49 patients who follow the breast–bone–lung path, the probability regardless of immunohistochemistry characteristics of a given of transitioning to the “deceased” state is small (roughly 0.02). The tumor or overall survival, all deceased patients died after an highest next transition is to liver for this group (transition average of four metastatic sites. probability roughly 0.55). By contrast, the group who follow the breast–bone–liver pathway’s highest next transition probability is Temporal distributions “deceased” (roughly 0.35), occurring on average roughly 2 years later. The most probable next transition for this group is to distant To link the discrete Markov time step “k” to the data, the temporal lymph nodes, with probability 0.31. distributions are shown in the panel in Figure 6. Figure 6a shows © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited npj Breast Cancer (2015) 15018 Spatiotemporal progression of metastatic breast cancer PK Newton et al Figure 6. Histograms showing average time from diagnosis to (a) first metastatic site, (b) second metastatic site, (c) bone metastasis, (d) chest wall metastasis, (e) lung metastasis, and (f) liver metastasis. Graphs are color coded for specific metastases (a and b) or met relapse number (c–f). A two-parameter Weibull distribution is used as a curve fit. the average time from diagnosis to first metastatic site, 5.30 years. important characteristic, with bone, mammary lymph nodes, and The histogram is well modeled by a two-parameter Weibull chest wall being the main spreaders for breast cancer, and distal distribution. Figure 6b shows the average time to the second lymph nodes, liver, and brain being sponges. However, the metastatic site from diagnosis, 7.58 years. Figures 6c–f show the spreader–sponge character does depend on ER/HER2 status; the average times to a bone metastasis (6.53 years), chest wall main example would be that lung/pleura are sponges for metastasis (6.02 years), lung metastasis (6.92 years), and liver HER2 − , but spreaders for HER2+. Whether or not this is because metastasis (7.72 years). All are well modeled by Weibull of differing treatments for these two groups is not clear. distributions. See the website http://kuhn.usc.edu/breast_cancer/ Although most clinicians will, from experience, know that for temporal distributions associated with different subgroups. certain anatomic distributions of disease are associated with worse outcomes, the model presented here suggests that there is significant interplay between organ distribution and hormone- DISCUSSION receptor status. Inclusion of therapeutics into the model, Analyzing longitudinal data in terms of its combined spatiotem- along with patient characteristics such as age, performance status, poral characteristics is an important step in building a compre- and genomic data has a potential to increase its complexity as hensive, robust, and predictive cancer progression model that can well as predictive power. Although highly attuned physicians serve as a framework for statistical forecasting. There are several may have the capacity to replicate the predictive ability of the key points that are brought out in the current model worth model, we anticipate that the performance of individual reiterating. The first metastatic site very strongly influences future physicians to predict patient outcomes will be variable. For non- prognosis, even as much as ER/HER2 status of the patient. Second, oncologists, a model such as this one may provide superior the spreader–sponge classification of the metastatic sites is an accuracy from the standpoint of prognosis. Moreover, noting that npj Breast Cancer (2015) 15018 © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited Spatiotemporal progression of metastatic breast cancer PK Newton et al despite immunohistochemistry subgroups, nearly all patients 7 Gneiting T, Raftery AE. Weather forecasting with ensemble methods. Science 2005; 310:248–249. approach death after four sites of metastatic disease may be 8 Bloom HJ, Richardson WW. Histological grading and prognosis in breast cancer; a clinically useful. study of 1409 cases of which 359 have been followed for 15 years. Br J Cancer Additional efforts to refine the model in the future should 1957; 11:359–377. include incorporation of therapeutic effects and the impact of 9 Sotiriou C, Neo SY, McShane LM, Korn EL, Long PM, Jazaeri A et al. 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Novel patterns of level of model development, future understanding of the role of genome rearrangement and their association with survival in breast cancer. disease volume in cancer spread is a necessary factor for future Genome Res 2006; 16: 1465–1479. development. 12 Minn AJ, Gupta GP, Siegel PM, Bos PD, Shu W, Giri DD et al. Genes that mediate The full data used to develop the model described in this breast cancer metastasis to lung. Nature 2005; 436:518–524. paper are quite comprehensive and are available for graphical 13 Kang Y, Siegel PM, Shu W, Drobnjak M, Kakonen SM, Cordón-Cardo C et al. user-controlled viewing on the website: (http://kuhn.usc.edu/ A multigenic program mediating breast cancer metastasis to bone. Cancer Cell 2003; 3:537–549. breast_cancer/). 14 Gupta GP, Massagué J. Cancer metastasis: building a framework. Cell 2006; 127: 679–695. 15 Nguyen DX, Bos PD, Massagué J. Metastasis: from dissemination to organ-specific ACKNOWLEDGMENTS colonization. Nat Rev Cancer 2009; 9:274–284. We are grateful to the Memorial Sloan Kettering Cancer Center for mining, 16 Nguyen DX, Massagué J. Genetic determinants of cancer metastasis. Nat Rev organizing, and supplying the data used in this project. Genet 2007; 8:341–352. 17 Kang Y, He W, Tulley S, Gupta GP, Serganova I, Chen CR et al. Breast cancer bone metastasis mediated by the Smad tumor suppressor pathway. Proc Natl Acad Sci CONTRIBUTIONS USA 2005; 102: 13909–13914. PN and JM wrote the main manuscript text. JM prepared Figures 1–6. NV and EC 18 Bos PD, Zhang XH, Nadal C, Shu W, Gomis RR, Nguyen DX et al. Genes that reviewed medical charts and finished consolidating the data. MJ initially presented mediate breast cancer metastasis to the brain. Nat Lett 2009; 459: 1005–1009. the data set. BH performed preliminary analysis of data. PN, JM, JN, EC, LN, and PK 19 Chiang AC, Massagué J. Molecular basis of metastasis. N Engl J Med 2008; 359: reviewed and edited the manuscript. 2814–2823. 20 Newton PK, Mason J, Bethel K, Bazhenova LA, Nieva J, Kuhn P. A stochastic Markov chain model to describe lung cancer growth and metastasis. PLoS One COMPETING INTERESTS 2012; 7: e34637. 21 Newton PK, Mason J, Bethel K, Bazhenova LA, Nieva J, Norton L et al. Spreaders The authors declare no conflict of interest. and Sponges define metastasis in lung cancer: a Markov chain Monte Carlo Mathematical Model. Cancer Res 2014; 73: 2760–2769. 22 Bazhenova LA, Newton PK, Mason J, Bethel K, Nieva J, Kuhn P. Adrenal metastases FUNDING in lung cancer: clinical implications of a mathematical model. J Thorac Onc 2014; The project described was supported by a U54 NIH/NCI PS-OC Transnetwork Grant 9:442–446. from 1 September 2013 to 1 September 2014. The content is solely the responsibility 23 Newton PK, Mason J, Hurt B, Bethel K, Bazhenova LA, Nieva J et al. 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Robust- This work is licensed under a Creative Commons Attribution 4.0 ness, scalability, and integration of a wound-response gene expression signature International License. The images or other third party material in this in predicting breast cancer survival. Proc Natl Acad Sci USA 2005; 102: 3738–3743. article are included in the article’s Creative Commons license, unless indicated 6 Early Breast Cancer Trialists’ Collaborative Group (EBCTCG). Effects of che- otherwise in the credit line; if the material is not included under the Creative Commons motherapy and hormonal therapy for early breast cancer on recurrence and license, users will need to obtain permission from the license holder to reproduce the 15-year survival: an overview of the randomised trials. Lancet 2005; 365: material. 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Spatiotemporal progression of metastatic breast cancer: a Markov chain model highlighting the role of early metastatic sites

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Biomedicine; Biomedicine, general; Cancer Research; Oncology; Human Genetics; Cell Biology
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www.nature.com/npjbcancer All rights reserved 2374-4677/15 ARTICLE OPEN Spatiotemporal progression of metastatic breast cancer: a Markov chain model highlighting the role of early metastatic sites 1,2 3 4 4 5 6 4 Paul K Newton , Jeremy Mason , Neethi Venkatappa , Maxine S Jochelson , Brian Hurt , Jorge Nieva , Elizabeth Comen , 4 3 Larry Norton and Peter Kuhn BACKGROUND: Cancer cell migration patterns are critical for understanding metastases and clinical evolution. Breast cancer spreads from one organ system to another via hematogenous and lymphatic routes. Although patterns of spread may superficially seem random and unpredictable, we explored the possibility that this is not the case. AIMS: Develop a Markov based model of breast cancer progression that has predictive capability. METHODS: On the basis of a longitudinal data set of 446 breast cancer patients, we created a Markov chain model of metastasis that describes the probabilities of metastasis occurring at a given anatomic site together with the probability of spread to additional sites. Progression is modeled as a random walk on a directed graph, where nodes represent anatomical sites where tumors can develop. RESULTS: We quantify how survival depends on the location of the first metastatic site for different patient subcategories. In addition, we classify metastatic sites as “sponges” or “spreaders” with implications regarding anatomical pathway prediction and long-term survival. As metastatic tumors to the bone (main spreader) are most prominent, we focus in more detail on differences between groups of patients who form subsequent metastases to the lung as compared with the liver. CONCLUSIONS: We have found that spatiotemporal patterns of metastatic spread in breast cancer are neither random nor unpredictable. Furthermore, the novel concept of classifying organ sites as sponges or spreaders may motivate experiments seeking a biological basis for these phenomena and allow us to quantify the potential consequences of therapeutic targeting of sites in the oligometastatic setting and shed light on organotropic aspects of the disease. npj Breast Cancer (2015) 1, 15018; doi:10.1038/npjbcancer.2015.18; published online 21 October 2015 INTRODUCTION all are based (typically) on a single snapshot of patient information in time and mostly obtained only at the primary tumor location It is widely appreciated that cancer is a multifaceted disease when clinically detectable, hence have limited predictive power comprised of distinct biochemical, biomechanical, molecular, age, with respect to forecasting of disease progression and survival. In gender, race, and environmental factors, all of which contribute other forecasting settings (e.g., weather prediction), it is widely directly or indirectly to uncontrolled cell growth, survival, motility, 1–5 appreciated that collecting data at multiple spatial locations and dissemination, and colonization, which in turn effect long-term at multiple time points gives far superior forecasting capability survival of patients. The complex interplay of all of these factors is (even if at lower resolution than a single site) as from these, one is poorly understood, which hinders our ability to accurately predict able to obtain estimates of time derivatives (velocities), and spatial and optimally influence outcomes throughout the course of gradients, facilitating better estimates not just of the current disease progression. As breast cancer spreads from one organ to localized state, but the future distributed state. another via hematogenous and lymphatic routes, cell migration In this paper, we explore the possibility that although breast patterns are critical for understanding metastasis and clinical cancer progression in individuals where little additional clinical evolution, but these patterns are commonly dismissed as information is known can be viewed as unpredictable, metastasis unpredictable in the absence of detailed clinical and patient- patterns assembled over populations of patients that incorporate specific contextual information. As a consequence, comprehensive quantitative statistical forecasting tools to aid in medical decision both temporal and spatial information can be used as a firm basis making have been slower to develop than in other fields, such as for predictive modeling and provides an essential step in financial forecasting and weather prediction. For breast cancer, developing computer-assisted forecasting tools. One of the simplest and most effective dynamical modeling assumptions the main prognostic factors in current use include tumor size, used in this paper is the Markov assumption that progression from patient age, lymph node status, histologic type of tumor, pathologic grade, and hormone-receptor status, and when one anatomical location to another proceeds as a weighted 8–19 available, genetic profiling can also be used effectively. But random walk on a directed graph, with no history dependence 1 2 Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA, USA; Department of Mathematics, University of Southern California, 3 4 Los Angeles, CA, USA; Department of Biological Sciences, Dornsife College of Letters, Arts and Sciences, University of Southern California, Los Angeles, CA, USA; Memorial Sloan 5 6 Kettering Cancer Center, New York, NY, USA; University of Colorado School of Medicine, Aurora, CO, USA and Norris Comprehensive Cancer Center, Keck School of Medicine, University of Southern California, Los Angeles, CA, USA. Correspondence: PK Newton (newton@usc.edu) Received 8 September 2015; accepted 9 September 2015 © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited Spatiotemporal progression of metastatic breast cancer PK Newton et al other than the fact that the tumor initiates in the breast. Although Markov chains not exact, the Markov assumption has been used effectively for a A Markov chain dynamical system is a discrete-time stochastic process: 20–23 lung cancer data set. ! ! v ¼ v A; ðk ¼ 0; 1; 2; ¼Þ Formed by the longitudinal data set of 446 breast cancer kþ1 k patients from Memorial Sloan Kettering Cancer Center assembled ! where A is an nxn transition matrix and v is a state vector whose entries over a 25-year period, the Markov transition probabilities indicate the probability of a metastatic tumor developing at each of the n from site to site are estimated for each of the groups anatomical sites, at time step k. The time step k represents spread from estrogen receptor (ER)+/human epidermal growth factor receptor one site to the next in a patient, which can be calibrated with data. The 2 (HER2) −,ER − /HER2 − , and HER2+. We show that survival initial state vector in our model is given by v ¼ð1; 0; 0; 0; ¼ Þ, where the depends on the location and characteristics of the first metastatic first entry corresponds to the breast location, indicating that initially there is a tumor located in the breast with probability 1, and no other metastatic site to which the disease spreads. In fact, the data show that tumors at the other locations. The transition matrix A has entries whose survival characteristics that use this dynamical and spatial rows sum to one (corresponding to the fact that they represent information are potentially as predictive as the ER/HER2 status probabilities of transition and hence must sum to one), and the ijth entry, of a patient. Stated differently, we use information not only on a , indicates the probability of metastatic disease spreading from site “i” to ij static characteristics of the primary tumor taken as a snapshot in site “j”. We refer the reader to Norris for a comprehensive introduction to time but also dynamical information on where the disease is Markov chains and refs 20–23 for recent applications of Markov modeling spreading, and associated characteristics of the first metastatic in the context of lung cancer metastasis. As the longitudinal data are site. The location and character of this first site, in turn, have relatively time resolved over long periods, the entries of the transition important consequences on the locations and time sequence of matrix are obtained in a straightforward empirical way by simple subsequent metastatic sites, influencing timescales of disease denumeration of disease progression events from one anatomical site to the next in each of the patients in a cohort (see ref. 25 for more general progression and survival. The full panel of spatiotemporal discussions). For example, in tracking a cohort of 100 patients with a diagrams and models for each subgroup is available for further primary breast tumor only, if 36 of them subsequently develop their first study on the interactive website. Additional information metastatic tumor in the bone, then the transition probability from breast to associated with treatment scenarios is also available. bone, obtained empirically, would be 0.36 for this cohort. Note that this number should be interpreted as an estimate based on the length of time the cohort is being followed. In a similar way, by simple denumeration of MATERIALS AND METHODS the distinct metastatic transitions from site to site that each patient Description of data set follows, we can estimate the Markov transition probabilities from any given The time-resolved data contain annotated clinical information on 446 site to any other site to create the Markov transition matrix A, which drives patients from the time of their initial diagnosis of breast cancer between our model dynamics. 1975 and 2009 at Memorial Sloan Kettering Cancer Center. Notably, the majority of patients were originally diagnosed after 1990, with only 2 patients diagnosed initially in 1975 and 1979, and 25 patients diagnosed in the 1980s. RESULTS None of the patients had evidence of metastatic disease at the time of Ten-year progression pathways diagnosis; all of the patients eventually developed metastatic disease. For The panels in Figure 1a show ring diagrams associated with each patient, the database contains all clinical and demographic information 10-year progression representing all patients whom we have a on the patient from the date of their diagnosis and subsequent development of metastatic disease over time. For each patient, metastatic disease is noted minimum of 10 years of continuous data on starting at the time of at the time of diagnosis of metastatic disease, usually first detected by diagnosis. These include patients that were enrolled in the study positron emission tomography imaging and confirmed by biopsy. Patients for more than 10 years and those that were expired before the were then followed with serial positron emission tomography and/or 10-year mark (as we know their metastatic progression after their computed tomography imaging and physical exams. Physical exams were death date). For the remainder of the paper, we will only focus on usually done between 1- and 3-month intervals. Imaging was usually done at those patients that qualify for the 10-year study. The 10-year 3-month intervals. At the time of new metastatic development, site(s) of window was chosen as a balance between having enough disease and the date were noted. The treatment rendered and any other patients for statistical significance (i.e., not too long), yet long pertinent clinical and demographic information is available on each patient. All the relevant information regarding each patient’s original breast cancer enough so that significant progression occurred in the cohort diagnosis, including date of pathology report, type of breast cancer, and under study. The website http://kuhn.usc.edu/breast_cancer/ oncologic and surgical treatment rendered at original diagnosis is noted. All allows for interactive viewing of these diagrams for both shorter of the information on the treatment rendered throughout metastatic disease and longer windows. Figure 1a shows the pathways of the 350 course is documented. The date of last follow-up and whether patients are eligible patients all grouped together over the 10-year window. alive or deceased is also noted. Of the 446 patients, 173 patients were alive as For this group, bone metastases are the most prominent first of 5 January 2013 and 273 had expired. metastatic location, occurring in roughly 35% of the patients being followed. In Figure 2b–d we break the group down into Metastatic progression diagrams subcategories. Figure 1b shows the ER+/HER2 − subgroup Longitudinal data can be organized most usefully in the form of ring (218 patients), where bone metastasis occurs first in roughly diagrams, as shown in Figure 1a for the entire aggregated data set. Disease 40% of all patients. Figure 1c shows the ER − /HER2 − subgroup progression proceeds from the inner pink ring (primary breast tumor) (70 patients), where bone metastases occurs in a little over 25% of outward, with each ring representing a subsequent metastatic tumor, color the patients, and Figure 1d shows the HER2+ subgroup coded according to anatomical site, with a sector size representing the (62 patients) with ~ 33% of patients relapsing first at the bone percentage of patients with tumors at that location. The first ring out from the inner ring in Figure 1a shows that bone is the most prominent first site. Further examination of the sector sizes in the first metastatic metastatic site, in roughly 35% of the patients. The progression of each of ring shows that the second most common first relapse site differs the 350 patients proceeds along a ray. The diagram summarizes the among the subgroups. For the ER+/HER2 − and the ER − / complete pathway history (207 distinct pathways) associated with this HER2 − groups, distant lymph nodes are the second most common group of patients tracked over the duration of 10 years. From this data, we first metastatic site, whereas for the HER2+ subgroup, the second can compute the probability of disease “transition” from one anatomical most common first relapse site is lung/pleura, followed by chest site to any of the others, based on the statistical information contained in wall. The diagrams can be viewed from year to year as gif files on the diagrams. This allows us to estimate the entries of the Markov the interactive website, giving a dynamic view of the disease as it transition matrix associated with disease progression, both in bulk, and for subgroups, which we describe next. progresses from the central pink ring outward. npj Breast Cancer (2015) 15018 © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited Spatiotemporal progression of metastatic breast cancer PK Newton et al Figure 1. Spatiotemporal progression diagram over a 10-year period of subsets of breast cancer patients. The innermost to outermost rings show progression patterns of primary breast cancer patients (pink ring) and formation of metastases (subsequent rings). Circular arc length of each sector represents the percentage of patients with a metastatic tumor in that location. Bone (yellow) is the most common first metastatic site (first ring outside pink). (a) All Patients, (b) ER+/HER2 −,(c)ER − /HER2 − , and (d) HER2+. It should be noted that death is a relatively uncommon Kaplan–Meier curves outcome for a patient with a metastasis to a single organ site, Figure 2 shows Kaplan–Meier survival curves associated with the occurring in only 33.33% of patients in the overall cohort. Though 10-year cohort that we track. Figure 2a shows survival it was notably more common in the HER2+ subgroup of patients curves based on the three subgroups ER+/HER2 − (218 patients), with liver metastasis, and affected 100% of that subgroup. As ER − /HER2 − (70 patients), and HER2+ (62 patients). Note that the expected, the largest number of long-term survivors is recognized ER+/HER2 − subgroup and the HER2+ subgroup show better as ER+/HER2 − patients with bone-only metastasis, with 91.67% of survival trends than the ER − /HER2 − group. these patients remaining alive during the median 10 years of Survival times are measured from the time of initial breast follow-up. Unexpectedly, we also identified that patients with their cancer diagnosis and not from the time of the development of first site of metastasis to lung-only metastasis had a favorable metastatic disease. Patients were treated with Memorial Sloan percentage of patients going on to be long-term survivors Kettering Cancer Center standard of care or appropriate clinical with 68.97% of this subgroup surviving to the end of the trial-based therapy depending on physician recommendations 10-year study period. Of note, the majority of the patients with and patient preferences. Of the HER2+ patients, 87.10% received single lung metastasis as their first presentation of metastasis had trastuzumab-based therapy at some point during their disease ER+/HER2 − disease, only 5 of the patients with a single course. HER2+ patients diagnosed before 15 May 2005 did not lung metastasis at first presentation had triple-negative routinely receive trastuzumab in the adjuvant setting. After this disease. Interestingly, while many of these patients had lung date, most patients did receive herceptin in the adjuvant setting, biopsies to confirm metastatic breast cancer as opposed to a which was noted to significantly improve the outcomes for HER2+ primary lung cancer, they did not routinely undergo resection of breast cancer patients. In the metastatic setting, the Food and the lung metastasis or radiation to the lung. Long-term Drug Administration originally approved trastuzumab in Septem- survivors were also identified in 60.00% of patients with isolated liver metastasis. ber of 1998 (ref. 27). All of the ER+ patients received some form of © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited npj Breast Cancer (2015) 15018 Spatiotemporal progression of metastatic breast cancer PK Newton et al Figure 2. Kaplan–Meier curves showing the survival of breast cancer patients when they initially have no evidence of metastasis to when they progress through their metastatic disease. (a) Comparison of ER+/HER2 −,ER − /HER2 − , and HER2+ patients, (b) patients with a solitary first metastatic site at bone, chest wall, liver, or brain, and (c) subsets of patients with different numbers of first relapse metastases. npj Breast Cancer (2015) 15018 © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited Spatiotemporal progression of metastatic breast cancer PK Newton et al Figure 3. Markov chain networks of metastatic breast cancer shown as circular chord diagrams. Chord widths at their respective starting locations represent one-step transition probabilities between two sites. Primary breast cancer is located on top with metastatic sites ordered clockwise in decreasing order according to transition probability from primary. (a) All patients’ network, (b) all patients’ network highlighting paths connected to the breast, (c) all patients’ network highlighting paths connected to the bone, and (d) all patients’ network highlighting paths connected to deceased. endocrine therapy during the course of their treatment as good an indicator of survival as groupings associated with (i.e.,—tamoxifen, aromatase inhibitor, faslodex). ER/HER2 status. Figure 2c shows survival of patients with multiple Figure 2b shows survival trends based not on these subgroups, early metastases to various sites. Poorest survival are those with but on groupings associated with the location of the first multiple (more than two) first metastases, while much better metastatic site. We focus on four main metastatic sites being survival characteristics are associated with those patients with first bone (87 patients), chest wall (54 patients), liver (21 patients), and metastases that are solitary. brain (5 patients). The patients with first mets to the chest wall The hazard rate of a Kaplan–Meier curve indicates the rate at have the best prognosis, whereas those with first mets to the brain which survival probability is decreasing within the population have the poorest prognosis. Although the 5-year survival of being studied. Computing the hazard ratio between two survival patients with a bone first met is equal to those with a chest wall curves is a good measure of how much better or worse a certain met (around 85%), the 10-year survival is much worse for chest subgroup is doing compared with another. For example, if group wall patients as compared with bone patients (50% vs. 70%, A dies at twice the rate of group B, then the hazard ratio respectively). Patients with first mets at the liver have a poor would be 2. 10-year survival rate (~30%). Definition of a metastasis was based on global clinical Markov chain networks and spreader–sponge diagrams evaluation, which included imaging results, physical examination, Figure 3 shows the Markov diagrams whose transition values are and in many cases, biopsy. However, tissue confirmation of a obtained from the data depicted in the ring diagrams of Figure 1a. metastatic site was not required for the purposes of the model. The breast site is listed at 12:00 in these diagrams, followed in A comparison of Figure 3a, b generally shows that groupings associated with first metastatic location (Figure 2b) gives at least clockwise decreasing order by the most likely first metastatic sites © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited npj Breast Cancer (2015) 15018 Spatiotemporal progression of metastatic breast cancer PK Newton et al Figure 4. Pathway diagrams showing top 30 two-step pathways emanating from breast (pink ring). Nodes are classified as a “spreader” (red) or “sponge” (blue) based on the ratio of the incoming and outgoing two-step probabilities (spreader and sponge factor listed in respective ovals). (a) All patients’ pathway diagram representing 79.8% of total pathways, (b) ER+/HER2 − pathway diagram representing 83.0% of total pathways, (c)ER − /HER2 − pathway diagram representing 81.9% of total pathways, and (d) HER2+ pathway diagram representing 85.5% of total pathways. the patients aggregated (Figure 4a), bone, chest wall, and from the breast. Figure 3a shows the full network diagram clearly depicting the systemic interconnectedness of the anatomical sites mammary lymph nodes are the spreader sites, and lung/pleura, throughout the course of the disease. In these diagrams we also distant lymph nodes, and liver are the sponge sites. In use “deceased” as one of the states in the model and list it in the Figure 4b we show the ER+/HER2 − subgroup with the same last position. The thickness of the paths leaving each of the sites spreader/sponge sites. The amplification factor of bone for this indicates the proportion of transitions from that site to the subgroup (5.421) is particularly high, whereas the absorption receiving site. To clarify this further, we show the outgoing paths factor for liver (0.166) is quite low. For the ER − /HER2 − group from breast (Figure 3b) and bone (Figure 3c). In Figure 3d we show shown in Figure 4c, the mammary lymph nodes seem to be the the paths incoming to the deceased site. strongest spreader (amplification factor of 5.778). Also of some Although the patterns of metastatic spread appear to be highly significance is the brain in this subgroup becomes a sponge, with complex, they can be simplified by examination of respective an absorption factor of 0.392. For the HER2+ subgroup shown in components. The finding on Figure 3b showing that the pathways Figure 4d, lung/pleura and chest wall become the main spreaders, that breast cancer takes out of the breast is significantly less aside from bone. To clarify the spreader/sponge paths more complex than the overall model in Figure 4a suggests that not clearly, Figure 5a–f shows the paths exiting from each of the main only is the primary tumor a source for metastasis but also spreaders (all category), and each of the main sponges. Figure 6a, metastases themselves serve as sources of other metastatic sites d, when viewed together, are instructive in that they show direct and many of these secondary metastases are associated with high significant exchange between spreaders and sponges. For risk of transitioning to death as shown in Figure 3d. example, Figure 5a shows that lung/pleura is the most probable Figure 4 shows the reduced spreader–sponge diagrams for all (sponge) site when exiting bone. Figure 5d, on the other hand, of the patients (Figure 4a), followed by diagrams for each of the shows that cells that exit the lung/pleura site most probably go to subgroups ER+/HER2 −,ER − /HER2 − , HER2+. Sites colored in red liver, another sponge, but they can also go back to bone. are “spreader” sites, whose ratio of outgoing path probability to Prior animal and human experiments have supported the incoming path probability (called the amplification factor) is concept that metastatic sites are seeded and re-seeded with travel greater than one, whereas those colored blue are “sponge” sites, of cancer cells from one site to another via hematogenous 20–21,28 whose ratio of outgoing path probability to incoming path routes; hence flow of cancer cells is likely to be bidirectional probability (called the absorption factor) is less than one. For all of for all metastatic sites. However, the net flow will generally be in npj Breast Cancer (2015) 15018 © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited Spatiotemporal progression of metastatic breast cancer PK Newton et al Figure 5. Spreader/sponge diagrams for all patients showing one-step transition probability from (a) bone, (b) chest wall, (c) LN (mam), (d) lung/pleura, (e) LN (dist), and (f) liver to the top nine sites in the network. Sites are ordered in decreasing order, clockwise, with the spreader/ sponge in question located at 12:00. Outer pink ring represents primary breast cancer and shows the percentage of total transition probability it represents. dist, distant; LN, lymph node; mam, mammary. Of note, very few of these patients underwent pulmonary or the direction from spreader sites to sponge sites. Although therapeutic interventions such as radiotherapy and hormonal hepatic resection or radiotherapy directed at a single organ site. therapy may have the ability to impact trafficking of tumor sites, We suspect that the more likely cause of this difference may be the model did not incorporate differential effects of therapy into the spreader/sponge characteristics of these tumor types in the model and the gradient of metastatic growth is modeled metastatic breast cancer patients. If one examines subgroups, it is based on the population average and standard-of-care noted that for all groups except the triple-negative population, the interventions. An understanding of the impact of therapeutics liver is a more powerful sponge than the lungs, with smaller on the spreader and sponge characteristics of local sites requires transition probabilities for liver than lung in the ER+ and/or HER2+ further investigation. groups. It is within the ER+ and HER2+ groups that there is a low probability of transition from lung metastasis to death, whereas in the triple-negative group, where the transition probability is Metastatic relapse data higher for liver than for lungs that we see an increased risk of It is interesting to go further out in the pathway diagrams. death following development of a lung metastasis. Although in Figure 1a shows that after developing a metastatic tumor at the the absence of a second validation data set, it is possible that bone site, the two most probable second metastatic sites are these findings are artifactual, they raise the possibility that organs lung/pleura, and liver, both representing roughly equal sector that are more “sponge-like” relative to other affected organs are widths (around 10%). But the future prognoses associated with the anatomic sites at highest risk for organ failure leading to those two groups of patients are quite different. In the case of the death. This is particularly true for visceral sites. Interestingly, 49 patients who follow the breast–bone–lung path, the probability regardless of immunohistochemistry characteristics of a given of transitioning to the “deceased” state is small (roughly 0.02). The tumor or overall survival, all deceased patients died after an highest next transition is to liver for this group (transition average of four metastatic sites. probability roughly 0.55). By contrast, the group who follow the breast–bone–liver pathway’s highest next transition probability is Temporal distributions “deceased” (roughly 0.35), occurring on average roughly 2 years later. The most probable next transition for this group is to distant To link the discrete Markov time step “k” to the data, the temporal lymph nodes, with probability 0.31. distributions are shown in the panel in Figure 6. Figure 6a shows © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited npj Breast Cancer (2015) 15018 Spatiotemporal progression of metastatic breast cancer PK Newton et al Figure 6. Histograms showing average time from diagnosis to (a) first metastatic site, (b) second metastatic site, (c) bone metastasis, (d) chest wall metastasis, (e) lung metastasis, and (f) liver metastasis. Graphs are color coded for specific metastases (a and b) or met relapse number (c–f). A two-parameter Weibull distribution is used as a curve fit. the average time from diagnosis to first metastatic site, 5.30 years. important characteristic, with bone, mammary lymph nodes, and The histogram is well modeled by a two-parameter Weibull chest wall being the main spreaders for breast cancer, and distal distribution. Figure 6b shows the average time to the second lymph nodes, liver, and brain being sponges. However, the metastatic site from diagnosis, 7.58 years. Figures 6c–f show the spreader–sponge character does depend on ER/HER2 status; the average times to a bone metastasis (6.53 years), chest wall main example would be that lung/pleura are sponges for metastasis (6.02 years), lung metastasis (6.92 years), and liver HER2 − , but spreaders for HER2+. Whether or not this is because metastasis (7.72 years). All are well modeled by Weibull of differing treatments for these two groups is not clear. distributions. See the website http://kuhn.usc.edu/breast_cancer/ Although most clinicians will, from experience, know that for temporal distributions associated with different subgroups. certain anatomic distributions of disease are associated with worse outcomes, the model presented here suggests that there is significant interplay between organ distribution and hormone- DISCUSSION receptor status. Inclusion of therapeutics into the model, Analyzing longitudinal data in terms of its combined spatiotem- along with patient characteristics such as age, performance status, poral characteristics is an important step in building a compre- and genomic data has a potential to increase its complexity as hensive, robust, and predictive cancer progression model that can well as predictive power. Although highly attuned physicians serve as a framework for statistical forecasting. There are several may have the capacity to replicate the predictive ability of the key points that are brought out in the current model worth model, we anticipate that the performance of individual reiterating. The first metastatic site very strongly influences future physicians to predict patient outcomes will be variable. For non- prognosis, even as much as ER/HER2 status of the patient. Second, oncologists, a model such as this one may provide superior the spreader–sponge classification of the metastatic sites is an accuracy from the standpoint of prognosis. Moreover, noting that npj Breast Cancer (2015) 15018 © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited Spatiotemporal progression of metastatic breast cancer PK Newton et al despite immunohistochemistry subgroups, nearly all patients 7 Gneiting T, Raftery AE. Weather forecasting with ensemble methods. Science 2005; 310:248–249. approach death after four sites of metastatic disease may be 8 Bloom HJ, Richardson WW. Histological grading and prognosis in breast cancer; a clinically useful. study of 1409 cases of which 359 have been followed for 15 years. Br J Cancer Additional efforts to refine the model in the future should 1957; 11:359–377. include incorporation of therapeutic effects and the impact of 9 Sotiriou C, Neo SY, McShane LM, Korn EL, Long PM, Jazaeri A et al. 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Nat Rev Cancer 2009; 9:274–284. We are grateful to the Memorial Sloan Kettering Cancer Center for mining, 16 Nguyen DX, Massagué J. Genetic determinants of cancer metastasis. Nat Rev organizing, and supplying the data used in this project. Genet 2007; 8:341–352. 17 Kang Y, He W, Tulley S, Gupta GP, Serganova I, Chen CR et al. Breast cancer bone metastasis mediated by the Smad tumor suppressor pathway. Proc Natl Acad Sci CONTRIBUTIONS USA 2005; 102: 13909–13914. PN and JM wrote the main manuscript text. JM prepared Figures 1–6. NV and EC 18 Bos PD, Zhang XH, Nadal C, Shu W, Gomis RR, Nguyen DX et al. Genes that reviewed medical charts and finished consolidating the data. MJ initially presented mediate breast cancer metastasis to the brain. Nat Lett 2009; 459: 1005–1009. the data set. BH performed preliminary analysis of data. PN, JM, JN, EC, LN, and PK 19 Chiang AC, Massagué J. Molecular basis of metastasis. N Engl J Med 2008; 359: reviewed and edited the manuscript. 2814–2823. 20 Newton PK, Mason J, Bethel K, Bazhenova LA, Nieva J, Kuhn P. A stochastic Markov chain model to describe lung cancer growth and metastasis. PLoS One COMPETING INTERESTS 2012; 7: e34637. 21 Newton PK, Mason J, Bethel K, Bazhenova LA, Nieva J, Norton L et al. Spreaders The authors declare no conflict of interest. and Sponges define metastasis in lung cancer: a Markov chain Monte Carlo Mathematical Model. Cancer Res 2014; 73: 2760–2769. 22 Bazhenova LA, Newton PK, Mason J, Bethel K, Nieva J, Kuhn P. Adrenal metastases FUNDING in lung cancer: clinical implications of a mathematical model. J Thorac Onc 2014; The project described was supported by a U54 NIH/NCI PS-OC Transnetwork Grant 9:442–446. from 1 September 2013 to 1 September 2014. The content is solely the responsibility 23 Newton PK, Mason J, Hurt B, Bethel K, Bazhenova LA, Nieva J et al. 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Robust- This work is licensed under a Creative Commons Attribution 4.0 ness, scalability, and integration of a wound-response gene expression signature International License. The images or other third party material in this in predicting breast cancer survival. Proc Natl Acad Sci USA 2005; 102: 3738–3743. article are included in the article’s Creative Commons license, unless indicated 6 Early Breast Cancer Trialists’ Collaborative Group (EBCTCG). Effects of che- otherwise in the credit line; if the material is not included under the Creative Commons motherapy and hormonal therapy for early breast cancer on recurrence and license, users will need to obtain permission from the license holder to reproduce the 15-year survival: an overview of the randomised trials. Lancet 2005; 365: material. To view a copy of this license, visit http://creativecommons.org/licenses/ 1687–1717. by/4.0/ © 2015 Breast Cancer Research Foundation/Macmillan Publishers Limited npj Breast Cancer (2015) 15018

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npj Breast CancerSpringer Journals

Published: Oct 21, 2015

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